Repeatability of simultaneous 3D 1H MRF/23Na MRI in brain at 7 T

Proton MRI can provide detailed morphological images, but it reveals little information about cell homeostasis. On the other hand, sodium MRI can provide metabolic information but cannot resolve fine structures. The complementary nature of proton and sodium MRI raises the prospect of their combined use in a single experiment. In this work, we assessed the repeatability of normalized proton density (PD), T1, T2, and normalized sodium density-weighted quantification measured with simultaneous 3D 1H MRF/23Na MRI in the brain at 7 T, from ten healthy volunteers who were scanned three times each. The coefficients of variation (CV) and the intra-class correlation (ICC) were calculated for the mean and standard deviation (SD) of these 4 parameters in grey matter, white matter, and cerebrospinal fluid. As result, the CVs were lower than 3.3% for the mean values and lower than 6.9% for the SD values. The ICCs were higher than 0.61 in all 24 measurements. We conclude that the measurements of normalized PD, T1, T2, and normalized sodium density-weighted from simultaneous 3D 1H MRF/23Na MRI in the brain at 7 T showed high repeatability. We estimate that changes > 6.6% (> 2 CVs) in mean values of both 1H and 23Na metrics could be detectable with this method.

www.nature.com/scientificreports/ practice, these challenges result in low-resolution images and long scan times (due to data averaging) required to increase SNR, and necessitates supplementary high-resolution proton ( 1 H) scans for anatomical reference 14 .
The idea of simultaneous multinuclear MRI was proposed in 1986 15 , but the first truly simultaneous implementations did not appear until the last decade [16][17][18][19][20] . Recently, we presented the first multinuclear method that simultaneously acquires sodium images and proton multi-parametric maps (normalized PD, T 1 , T 2, and B 1 + ) based on MRF 21,22 . The simultaneous acquisition of 1 H and 23 Na allows for a natural co-registration between images with high-resolution structural information from 1 H and images with low-resolution metabolic information from 23 Na.
After the development of a novel method, it is fundamental to realize a repeatability study to determine the sensitivity of the method to detect changes over time in longitudinal studies, or between subjects in transversal studies. Due to the unique characteristics of our method: simultaneous acquisition, pulse sequences and k-space sampling (MRF full radial for 1 H and MRI center-out radial for 23 Na), image reconstruction (dictionary and non-uniform FFT), and MRI equipment (magnet, coils, receiver), this study is still necessary even when previous works already assessed the repeatability of MRF 23,24 and sodium MRI 25 separately and in different data acquisition circumstances.
In this work, we assessed the repeatability of the quantification of normalized PD, T 1 , T 2 , and normalized 23 Na density-weighted measured from simultaneous 3D 1 H MRF/ 23 Na MRI acquisitions 22 in the brain at 7 T. Figure 1 shows one slice of the 1 H maps and 23 Na images from the 3 scans of subject 1 after co-registration and masking. Figure 2 shows one selected slice of the 1 H maps and 23 Na images from the first scan of each subject after co-registration, using the maps from the subject 1 as a reference, and masking. Figure 3 shows the brain segmentation in gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) of scan 1 for subject 1. Table 1 summarizes the results of the statistical analysis for all tissues and all scans, where Mean all and SD all are the mean value and standard deviation calculated over all the data, Inter-Var is the inter-subject variation, Intra-Var is the mean intra-subject variation, CV is the mean coefficient of variation and ICC is the intra-class variation. Figure 1S in supplementary information shows images from subject 2 along the 3 axes.

Results
As a general result, we can highlight that the mean CV was lower than 6.9% and the ICC was higher than 0.61 for all the 24 statistical results, mean and standard deviation (SD) of all 4 measurements in 3 brain regions.
Normalized PD. As the PD was normalized by the mean CSF intensity, the normalized PD value for the CSF was defined as 1.00. We observed that mean normalized PD over the 30 scans had a mean all ± SD all of 0.87 ± 0.04 for GM and 0.66 ± 0.03 for WM. The CV values were lower than 2.6% for the mean values, and within the range 4.4-4.7% for the SD values. The estimated ICC values were within the range of 0.62-0.74.     www.nature.com/scientificreports/

Discussion
As already observed in Yu et al. 22 , the measured mean T 1 and T 2 values in this study showed discrepancies with other results from the literature [26][27][28][29] . In particular, the T 1 values are approximately 20% lower than usually measured. A possible explanation for this discrepancy could be due to magnetization transfer (MT) effects 30 , which might be addressed by including MT as an additional dimension in the MRF dictionary. The T 2 values were also approximately 20% lower than usually measured. Systematic reductions in T 2 values have been reported in many previous MRF implementations 29,30 . Nonetheless, these discrepancies should not affect the ability of the method to detect intra-subject or inter-subject variations when the same sequence is applied to all subjects. Due to our specific normalization, it is unfeasible to compare the calculated values from the normalized PD and normalized Na 23 density-weighted with the literature. However, the fact that the proton and sodium density of the CSF shows a higher concentration, followed by the GM, and WM is consistent with previous works 26,32 .
The CVs associated with the mean values were much lower than the CVs obtained for the SD values. This suggests that the mean value is a more sensitive variable to detect changes over time or between subjects. Moreover, the CVs in CSF were higher than the CVs in GM and WM. This can be related with the fact that the CSF is more sensitive to segmentation errors due to the coarse slice thickness and partial volume effects. This behavior was also observed by Leroi et al. 26 .
The CVs obtained for the mean values of the T 1 , T 2 , and normalized PD were in the same range as the CVs measured in previous repeatability studies on 3D MRF methods. For example, Buonincontri et al. 24 measured CVs in the range of 07-1.3% for T 1 , 2.0-7.8% for T 2 , and 1.4-2.5% for normalized PD for the repeatability of 3D MRF in the healthy human brain at 1.5 T and 3 T. This study also showed the highest CVs for CSF, similarly to our current findings.
In summary, CVs and ICCs showed good to very good results (CV values lower than 6.9% and ICCs values higher than 0.61) over the 24 measurements. All of the variables (mean and SD of normalized PD, T 1 , T 2 , normalized 23 Na density-weighted in all 3 tissues) could therefore be considered for detecting changes over time in individuals (intra-subject variations) and differences between subjects (inter-subject variations). To be on the conservative side, we can estimate that this method should be able to detect changes greater than the double of the CVs. Considering only the mean value, which is the most sensitive variable, our method should detect variations > 5.2% for PD in GM and WM, > 1.0% for T 1 in GM and WM, > 5.2% for T 1 in CSF, > 1.2 for T 2 in GM and WM, > 6.4% for T 2 in CSF, > 5.0% for Na 23 density in GM and WM, and > 6.6% for 23 Na density in CSF.
We found that simultaneous 3D 1 H MRF/ 23 Na MRI is highly repeatable for T 1 and T 2 measurements, but less repeatable for normalized PD and normalized 23 Na density-weighted. This is most likely due to the fact that T 1 and T 2 were estimated based on the unique shape of signal dynamics (fingerprint), whereas PD and sodium density were estimated from the signal amplitude. Although the method accounts for transmit field (B 1 + ) inhomogeneity, other inhomogeneities from the receive field (B 1 -) or from B 0 , which were not corrected in the present study, as well as pre-amplifier gain variations, can still induce non-negligible bias in the signal amplitudes.

Conclusion
In this work, we assessed the repeatability of the mean value and SD of normalized PD, T 1 , T 2 , and normalized 23 Na density-weighted measurements in GM, WM and CSF, measured from simultaneous 3D 1 H MRF/ 23 Na MRI acquisition in 10 different subjects at 7 T (3 scans/subject). We showed that the overall repeatability was deemed very good, where CVs were lower than 6.9% and ICCs were higher than 0.61 in all 24 statistical measurements. We found out that the mean value of the measurements is a more sensitive metric than their respective SD (CV of mean values ≤ 3.3% for all measurements), and that this method should therefore be able to measure changes (inter-and intra-subject variations) > 6.6% (> 2 × CV) in normalized PD, T 1 , T 2 , and normalized 23 Na density-weighted images. In future works, we will implement the method to study patients with neuropathologies compared to healthy controls in transversal studies, and over time in the same subjects in longitudinal studies.

Materials and methods
Volunteers and scanning protocol. Ten healthy volunteers (5 men, 5 women, mean age = 34.6 ± 10.4 years) were scanned three times in two sessions within a week. In the first session, the volunteers were scanned twice, with a short break between the scans. During the break, the volunteers were asked to move the head position. The B 0 shim was recalibrated before the second scan. In the second session, the volunteers were scanned only once. The study was approved by the New York University Grossman School of Medicine institutional review board and was performed in accordance with the relevant guidelines and regulations set forth by the Human Research Protections Program. Informed consent was obtained before each scan session. MRI hardware. All experiments were performed at 7 T (MAGNETOM, Siemens, Erlangen, Germany) using a 16-channel-Transmit/Receive (8 proton channels + 8 sodium channels) dual-tuned 1 H/ 23 Na radiofrequency (RF) coil developed in-house 33 . An external frequency generator was inserted in the RF cabinet of the system to demodulate the sodium signal with a proper local oscillator 34 . This modification in the receiver chain allowed simultaneous acquisition of both proton and sodium signals, as described in more details in Yu et al. 21 .
Pulse sequence. The simultaneous 3D 1 H MRF/ 23 Na MRI sequence 22 was based on a "stack-of-stars" sampling scheme 35 . The nuclear spins were sequentially excited every TR (7.5 ms) for 1 H and every 2 TRs (15 ms) for 23 Na using non-selective pulses followed by one simultaneous readout for both nuclei. The 23 Na nuclei were excited every 2 TRs to make sure that a large effective spoiling moment can be obtained for the sodium acquisition part 22 . The phase encoding gradient moments were distributed such that images from both nuclei had the same slice thickness. The frequency encoding gradient moments were distributed such that a full radial www.nature.com/scientificreports/ trajectory for 1 H and a center-out radial trajectory for 23 Na were obtained in k-space, leading to a ratio of ~ 1.9 in in-plane resolution between the 1 H and 23 Na images. The full radial trajectory was chosen to minimize the effects of B 0 inhomogeneities in 1 H 22 . The SAR calculation contemplates both nucleus irradiations. More details about the simultaneous 3D 1 H MRF/ 23 Na MRI sequence can be found in Yu et al. 22 . A diagram of the sequence is shown in Fig. 4. The 3D simultaneous 1 H MRF/ 23 Na MRI sequence parameters were: FOV 240 × 240 × 168 mm 3 , 1 H 160 × 160/ 23 Na 84 × 84 matrix, 1 H 1.5 × 1.5 mm 2 / 23 Na 2.85 × 2.85 mm 2 in-plane resolution, 1 H TR = 7.5 ms/ 23 Na TR = 15 ms, 1 H TE = 2 ms/ 23 Na TE = 1 ms, 1 slab of 56 slices, 3 mm slice thickness for both 1 H and 23 Na, 6 shots per slab, total scan time 21 min. Data processing. The images were reconstructed and processed offline in MATLAB (Mathworks, Natick, MA, USA). The full-radial proton data and center-out sodium data were processed separately.
For proton MRF reconstruction, images were reconstructed with CG-SENSE 36 in order to reduce the radial artifacts 37 . The MRF dictionary was grouped and averaged with the same sliding window as CG-SENSE along the time domain 38 . The dictionary was computed using the extended phase graph (EPG) formalism 39 implemented in C++ 38 . Different step sizes were used for T 1 , T 2 , and B 1 + : T 1 ranged from 150 to 4347 ms, T 2 ranged from 15 to 435 ms, both incremented in steps of 5%; B 1 + ranged from 10° to 130°, in steps of 1°. The sodium MRI reconstruction was performed using non-uniform fast Fourier transform (NUFFT) 40 from all center-out radial samples combined into one single k-space dataset. A phase correction was applied to remove the phase drift between the MR system and the external frequency generator 22 .
All the images from the 3 scans for each volunteer were segmented in grey matter (GM), white matter (WM), and cerebrospinal fluid (CSF) tissue compartments with SPM 12 (UCL, London, UK) 41 . Tissue segmentation was performed using the PD, T 1 , and T 2 maps of each scan as input images. The tissue probability map outputs were then normalized and binarized with a threshold of 0.9 to minimize the number of pixels with multiple tissue components to generate non-overlapping GM, WM and CSF masks.
In order to realize a quantitative analysis, we normalized the proton and sodium density-weighted images. The PD map was normalized by the mean intensity of the CSF measured over the pixels of the CSF binarized mask to minimize partial volume effects (as described previously). The 23 Na density-weighted was normalized by the mean sodium intensity in the eyes (vitreous humor), which exhibited the maximum signal intensity in the sodium images. A manual ROI over the whole image volume that contains only the eyes was applied to calculate the mean eye intensity. The final sodium density-weighted image is therefore a normalized sodium www.nature.com/scientificreports/ density-weighted image that is proportional to some extent to the TSC. Nevertheless, this image should not be confounded with a TSC map since the effect of sodium relaxation times in different tissues were not measured nor mitigated by the acquisition (TE = 1 ms, TR = 15 ms, FA = 30°) in this case.

Statistical analysis.
As a first step in the statistical analysis, the masks were applied to all proton and sodium maps to calculate the mean value and the standard deviation of the normalized PD, T 1 , T 2, and normalized 23 Na density-weighted for each tissue (WM, GM and CSF) and each scan of each subject. We defined mean all and SD all as the mean and SD over all the data for each measurement respectively. We then calculated the mean intra-subject variance (the mean value of the variance between results from scans of the same subject) and the inter-subject variance (the variance between results from different subjects) of each measurement (mean and SD), see Eqs. 1 and 2.
where Intra_var(a) is the mean intra-subject variance for the measurement a , i represents a subject (i = 1 to N, with N = 10 subjects in this study), var i (a) is the variance of the measurement a for subject i , and Inter_var(a) is the inter-subject variance for the measurement a , mean i (a) is the mean value of the measurement a for subject i , and var is the variance among all the subjects. Finally, we computed the coefficient of variation (CV, in %) as expressed in Eq. 3 42 , and the intra-class correlation (ICC) as the inter-subject variance (inter-var) divided by the sum of the intra and inter variances 43 , see Eq. 4.
where CV (a) is the mean coefficient of variation for the measurement a expressed as percentage, SD i (a) is the standard deviation of the measurement a for subject i , and ICC(a) is the intra-class correlation for the measurement a.
The CV is considered an indicator of the utility of a measure for detecting within-subject changes over time. An ideal set of measurements has a CV equal to 0%. The ICC is a measure of the repeatability of the method. It has values between 0 and 1, where higher values are associated with more repeatable measurements. From the literature 44 , we can interpret that CV was regarded as very good if CV ⩽ 10%, good if 10% < CV ⩽ 20%, moderate if CV > 20%, and poor if CV > 30%. On the other hand, the ICC was regarded as very good if ICC ⩾ 0.8, good if 0.6 ⩽ ICC < 0.8, fair/moderate if 0.4 ⩽ ICC < 0.6, and poor if ICC < 0.4.

Data availability
The MRI datasets in this study are available upon request to the corresponding author. All measurements of normalized PD, T 1 , T 2 and normalized sodium density weighted data in GM, WM and CSF, for all scans and all subjects, are included in Supplementary material. (2) Inter var(a) = var(mean i (a)),